The realization of an inverse integral relationship between
atomic and hydration numbers respectively, in combination with the observation
of an improved order of agreement when atomic numbers are adjusted per unit
valence, led to Flint's adoption of use of Z+C as measure of relative mass, in
preference to Atomic Weight.

The below table (AW versus Z versus Z+C) exhibits
calculations of hydration numbers using each of three ions as the base ion (H+,
Rb+ or La+3) in each of three sets of calculations, inputting Atomic Weights,
versus Atomic Numbers, versus Atomic Numbers + Valence, respectively.
Thus, within the first set of calculations, that inputting Atomic Weights, for
the middle column using Rb+ as the base ion, the result is that which is also
illustrated in the paper "Direct Calculation of Hydration
Numbers for the Lighter Ions"; the other columns merely substitute H+ and
La+3 resp. as the base ion in place of Rb+; and the other sets of calculations
substitute Z or Z+C resp. for AW:

As is shown, the order of agreement between calculations using
all three base ions is clearly preferable using Z+C versus either Z or AW: